I have my IBM Slave clock working. This model has a 115V 60Hz synchronous motor, so it will run normally when connected to standard U. S. power. There is no provision for setting the clock, except by energizing the clutch magnet, which is a 115V coil.
I made a box in-line with the power cord having a button to manually activate the clutch magnet.
To advance the clock to the next hour, I activate the clutch magnet for more than 8 seconds (but less than 14) starting at XX:57:52.
To advance the clock to 6:00, I activate the clutch magnet for more than 14 seconds starting at 5:59:02.
I used to rebuild this style of clock, ours were 24 volt. we had a test box like the one you built.
I rebuilt them under the Simplex label.
Simplex bought out the Fire Alarm division and my guess the clocks as well.
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That motor has asbestos clutch packs and will last very long time, without corrections, it will last even longer.
The modern (non asbestos) version last 5-10 years. They also slightly changed the sector gear, meaning you need to replace it along with the motor.
We replaced all of our clocks with battery operated "atomic clocks". They last as long or longer than the motor and are cheaper.
Jim